The planar Lebwohl-Lasher appears when the lattice considered is two-dimensional. The square lattice is the usual choice for most of the simulation studies.
This system exhibits a continuous transition. The ascription of such a transition to the
Kosterlitz-Touless type is still under discussion
[8][9][10][11].

This model is the lattice gas version of the Lebwohl-Lasher model. In this case
the sites of the lattice can be occupied by particles or empty. The interaction
between nearest-neighbour particles is that of the Lebwohl-Lasher model.
This model has been studied in
[12].